AP EAPCET 05-Jul-2022 Shift 1 Paper

Equation of the given tangents are
‌E1=3x−4y+4=0
‌E2=6x−8y−7=0
‌⇒3x−4y−‌

7

2

=0
Here, a=3,b=−4c1=4,c2=‌

−7

2

Since, slopes of the given tangents are equal, i.e. ‌

3

4

.
∴ The given tangents are parallel,
‌d=|‌

c2−c1

√a2+b2

|=|‌

4−( −7 2 )

√32+(−4)2

|
‌d=‌

‌ 15 2

√9+16

=‌

15

2×5

=‌

3

2

As we know that distance between two parallel tangents of a circle is equal to the diameter of that circle.
∴‌ Diameter of given circle ‌=‌‌

3

2

∴‌ Radius of the given circle ‌‌=‌

‌ Diameter ‌

2

‌=(‌

3∕2

2

)=‌

3

4